Consistent modeling of scalar mixing for presumed, multiple parameter probability density functions

In this Brief Communication we describe a consistent method for calculating the conditional scalar dissipation (or diffusion) rate for inhomogeneous turbulent flows. The model follows from the transport equation for the conserved scalar probability density function (PDF) using a gradient diffusion closure for the conditional mean velocity and a presumed PDF depending on any number of mixture fraction moments. With the presumed β PDF, the model is an inhomogeneous modification to the homogeneous model of Girimaji ["On the modeling of scalar diffusion in isotropic turbulence," Phys. Fluids A 4, 2529 (1992)]. An important feature of the model is that it makes the classical approach to the conditional moment closure completely conservative for inhomogeneous flows